Yesenia Obrien

Answered

2022-07-14

I have a circle with an arc beginning at point (x,y). The radius is r, the arc angle(w/ respect to center) is $\theta $. How do I calculate the end point of the arc (a,b) ?

I know that the arc-length=radius*(arc angle)

I can't seem to find an easy way to solve this, I think the way to go is with parametric equations but I'm not sure.

I know that the arc-length=radius*(arc angle)

I can't seem to find an easy way to solve this, I think the way to go is with parametric equations but I'm not sure.

Answer & Explanation

Sophia Mcdowell

Expert

2022-07-15Added 14 answers

One way is to calculate the angle to the first point

$\alpha =\mathrm{arctan}\left(\frac{p1.y-cp.y}{p1.x-cp.x}\right)$

Then you add your angle and calculate the new point:

$p2.x=cp.x+r\ast cos(\alpha +\theta )$

$p2.y=cp.y+r\ast sin(\alpha +\theta )$

$\alpha =\mathrm{arctan}\left(\frac{p1.y-cp.y}{p1.x-cp.x}\right)$

Then you add your angle and calculate the new point:

$p2.x=cp.x+r\ast cos(\alpha +\theta )$

$p2.y=cp.y+r\ast sin(\alpha +\theta )$

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